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Discussion 5 to Talk Back 12
Re: Saint Anselm's Proof.

by Emmett Shear

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The author uses the phrase, "It goes like this: once you actually understand the argument, you can no more deny its premises than you can understand what a triangle is and deny that all three interior angles will add up to 180 degrees."

This is much more apt than you might think. I have no problem denying that the sum of the angles of a triangle add up to 180 degrees: draw it on a sphere. For further reading, this is called a non-euclidean geometry (in particular, this is elliptic or Riemannian geometry).

Once you accept the axioms of euclidean geometry, you cannot deny that it is true. The same goes for the ontological proof of god; having accepted its tenets you cannot deny its truth.

Unfortunately for the proof, there is no more reason to accept its tenets as true than accept Euclidean geometry as true. And before anyone states how obviously true it is that the angles of a triangle add up to 180 degrees, as far as we can tell elliptic geometry best describes the structure of our universe.



Coincidently, a squared circle is actually much easier to find than you would expect. Consider a square drawn onto a non-euclidian surface. The surface required to square a circle is more complicated than a sphere, but ultimately understandable. It is shaped like a 4 sided pyramid, only with the sides flexed inwards towards the center. Draw a square around the base; you will find that it is a circle (all points equidistant from the center at the top) and a square (four congruent line segments which meet at right angles).

The world is surprisingly flexible.